🤖 AI Summary
This study addresses the bias and uncertainty in parameter estimation arising from missing not at random (MNAR) data in linear multilevel models. The authors propose a sensitivity analysis approach that jointly models the outcome variable and the dropout mechanism, incorporating an interpretable sensitivity parameter. Under assumptions weaker than missing at random, this method enables partial identification of model parameters and constructs corresponding uncertainty intervals. To the best of our knowledge, this is the first integration of sensitivity analysis with multilevel modeling. The validity of the proposed approach is demonstrated through simulation studies, and its practical utility is illustrated in an empirical analysis examining the effects of loneliness and physical activity on memory trajectories, yielding robust and more interpretable inferences.
📝 Abstract
We propose a sensitivity analysis method for missing not at random (MNAR) data in the context of linear multilevel (mixed-effects) models. The outcome and dropout risk are both modelled using multilevel models and a bias adjustment due to MNAR data is derived. This bias can be estimated from observed data conditional on specified values of sensitivity parameter(s). Under the assumption that these parameters lie within a plausible range, the method partially identify the parameters of interest, yielding bounds for estimation and inference under assumptions weaker than missing at random. The proposed analysis is investigated in a simulation study and illustrated with an analysis of the association between loneliness and physical activity with memory trajectories, adjusting for demographic, socioeconomic, and health covariates.